GEST: A multi-scale dynamics-based reconstruction of global ocean surface current

Wang, Guiyu; Chen, Ge; Cao, Chuanchuan; Chen, Xiaoyan; Huang, Baoxiang

doi:https://doi.org/10.5194/essd-2023-107

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https://doi.org/10.5194/essd-2023-107

Preprints

05 Apr 2023

| 05 Apr 2023

Status: this preprint was under review for the journal ESSD but the revision was not accepted.

GEST: A multi-scale dynamics-based reconstruction of global ocean surface current

Guiyu Wang, Ge Chen, Chuanchuan Cao, Xiaoyan Chen, and Baoxiang Huang

Abstract. A high precision and fine resolution reconstruction of sea surface current is beneficial to the exploration of complicated ocean dynamic processes. Existing studies mainly use satellite sea level and wind stress fields to derive sea surface geostrophic and Ekman currents, and build physical inversion models for global or regional oceans. Despite the obvious success, there are a variety of typical dynamic processes in the ocean such as mesoscale eddies and small-scale waves, and any product of surface current that neglects the contribution of wave motion would be, at best, incomplete. In this context, we present a precise sea surface current product at 15 m depth named GEST (Geostrophic-Ekman-Stokes-Tide) by analyzing the coupling relationship between ocean surface components that correspond to different physical processes and the actual currents as observed by drifting buoys. The GEST was generated based on Ekman, geostrophic currents, and waved-induced Stokes drift and TPXO9 tidal currents. Specifically, in the calculation of Ekman currents, local applicability is taken into account to ensure that the friction layer of wind-driven current can reach where drifters could operate as normal. A comparison proves that combining multi-scale theory and the condition of local applicability improves estimation results by up to 3.6 cm/s compared with OSCAR product, and 0.3 cm/s with GlobCurrent. Furthermore, by comparing the reconstructed products with 1° and 0.25° resolution, we find that the higher resolution not only reveals more details of ocean currents especially mesoscale eddy energy associated with geostrophic currents, but also improves the accuracy by up to 5.62 cm/s.

Received: 25 Mar 2023 – Discussion started: 05 Apr 2023

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Guiyu Wang, Ge Chen, Chuanchuan Cao, Xiaoyan Chen, and Baoxiang Huang

Status: closed

RC1:
'Comment on essd-2023-107', Anonymous Referee #1, 25 May 2023
Review of the paper
GEST: A multi-scale dynamics-based reconstruction of global ocean surface current
By Guiyu Wang, Ge Chen, Chuanchuan Cao, Xiaoyan Chen , and Baoxiang Huang

General Comments
This paper presents a methodology to reconstruct ocean surface currents optimally combining different components of the ocean surface circulation : geostrophic, Ekman, tidal and wave-induced currents. Scientifically this work is sound, as it aims at providing a global surface currents product which can account locally for significant processes which could be missed relying only on a single/few of the aforementioned surface circulation components. I therefore recommend this paper for publication after considering the following major and minor issues:

Firstly, the metrics for evaluating the goodness of the data are mostly based on direct comparison with in-situ measured currents (drifting buoys), while the authors, already at the abstract level, mention the importance of both “high precision” and “fine resolution”. I think inserting additional analyses (e.g. spectral analyses based on Fast-Fourier-Transform) to evaluate the effective resolution of the GEST dataset could strengthen the manuscript (at least for the analyses presented in section 4.2);

While reading the results, I was concerned by the statistical significance of some of them. As an example, I may provide the specific case reported in figure 14 a. The RMSEs of the different datasets under evaluation are often few tenths of cm/s apart from each other. I was wondering if it is possible to add an information on the confidence level of the different RMSE computation (e.g. via bootstrap analysis). I think it could help readers understand when the GEST RMSE value is confirming the higher accuracy compared to other available surface currents datasets:

I struggled a bit to understand why the Authors wish to provide a dataset with 1°X1° degrees spatial resolution. It was not that clear to me for which purposes/applications it was meant for. Could the Authors please explain?

Specific Comments
I would recommend to further clarify section 3. I honestly struggled a bit to understand that section 3 presents the building blocks of the GEST product. Inserting few lines explaining this concept would be beneficial for the paper;

I think the introduction is lacking part of the effort that has been done to reconstruct surface currents from tracers observations. I thus encourage the authors to consider few additional literature items (e.g. Bowen et al. 2002, Gonzalez-Haro et al. 2014, Liu et al. 2017, Rio and Santoleri 2018 and references therein) and insert few lines in the introduction;

In the manuscript, there are some images (see e.g. figs. 1,3,5) where you claim you are presenting information on 1°x1° boxes. It seems to me the information has somehow been further smoothed spatially. Could the Authors please clarify the reasons behind this choice or, at least, clarify that directly in the text?

A doubt is still related to figure 14 a/c/d: on average, it seems that the overall RMSE of GEST and Globcurrent datasets are equivalent in the latitudinal bands 30-50N and 40-60S, In particular, it seems that GEST and Globcurrent products show alternating better performances in the 30-50N band and equivalent performances in 40-60S band. Such areas are dominated by major current systems, thus relevant for assessing the quality of a surface current product. Could the authors please try to explain further such behaviour? I think it would be useful for users, in order to understand which dataset should be used for a specific study area/application;

Line 152-153: this sentence is unclear to me. Which dataset does not constitute a full independent validation for your reference field? Which reference field are the Authors referring to?

Line 159: What do you mean exactly with “ Ekman layer reaches the position of the drogued drifters position of the drogue drifters”? Are you referring to the vertical position of the drogue? If so, please specify;

Line 186: although one might guess what the Authors mean by “ocean components” I don’t think it is appropriate to mention that one can compare “ocean components and drifter observations. I’d ask the Authors to rephrase the sentence;

Figure 6: The legend should clearly mention what the Authors mean by the blue and red curves. Also, it seems the “Attenuation of experience” and theoretical formula are not precisely mentioned in the manuscript. This makes It hard to intercompare the figure with the findings reported in the text. Could the Authors please further clarify?

Line 203: reading the text it is not simple to understand what the Authors mean by “theoretical formula”. Is this equation 4? Please specify and, in addition, I would provide more details for the “empirical percentage method”, in order to help readers not familiar with that;

Line 224: “Geostrophic currents act as the primary mechanism that form the ocean surface current field”. I do not think it is appropriate to mention that the Geostrophic Currents are a mechanism that generate the ocean current field. I would rather say that they are a component of the total marine currents field;

Line 254: recalling what I mentioned in the “major comments” section. I would ask if the Authors could check whether this 0.3 cm/s RMS difference is significant or not;

Table 1: I would ask the Authors to apply a minor change to the Table: please add the name of each sub-region, in order to help the readers locating the different sub-regions in a global map;

Lines 266-271: would it make sense/be possible for the Authors to add a global map that emphasizes the choice of the different sub-models combinations used for the global reconstruction?

Figure 11/Line 290: I sincerely struggled a bit in understanding the meaning of synthetic vector/optimal vector. Could the Authors please further explain or harmonize the nomenclature of the variables?

Technical Comments
Line 78: Maybe I would say “ and the Globcurrent project products”;

Line 108-110 (and elsewhere if necessary): Please remove the acronym CMEMS , keep Copernicus Marine Service instead;

Line 201: “wavenumber k and wavelength ?” It seems this sentence is unfinished. Could the Authors please double check?

Figure 9: I would add x and y axes labels as Longitude and Latitude while It is redundant to repeat RMSE (cm/s) for each of the four subfigures;

“The OSCAR near-surface current with a grid size of 1°on a 5 days basis use the quasilinear, quasi-steady sea surface momentum equations and improve the equatorial algorithm by fitting…” should be modified as follows: “The OSCAR near-surface currents product, with a grid size of 1°on a 5 days basis, uses the quasilinear, quasi-steady sea surface momentum equations and improves the equatorial algorithm by fitting…”

References
Bowen, M. M., Emery, W. J., Wilkin, J. L., Tildesley, P. C., Barton, I. J., & Knewtson, R. (2002). Extracting multiyear surface currents from sequential thermal imagery using the maximum cross-correlation technique.
Journal of Atmospheric and Oceanic Technology, 19(10), 1665-1676.

González‐Haro, C., & Isern‐Fontanet, J. (2014). Global ocean current reconstruction from altimetric and microwave SST measurements. Journal of Geophysical Research: Oceans, 119(6), 3378-3391.

Liu, J., Emery, W. J., Wu, X., Li, M., Li, C., & Zhang, L. (2017). Computing ocean surface currents from GOCI ocean color satellite imagery. IEEE Transactions on Geoscience and Remote Sensing, 55(12), 7113-7125.

Rio, M. H., & Santoleri, R. (2018). Improved global surface currents from the merging of altimetry and sea surface temperature data. Remote sensing of Environment, 216, 770-785
Citation: https://doi.org/10.5194/essd-2023-107-RC1
- AC1: 'Reply on RC1', Guiyu Wang, 19 Jun 2023
  
  Thank you for your favourable recommendation. Please find our replies in the attachment.
  
  Citation: https://doi.org/10.5194/essd-2023-107-AC1
RC2:
'Comment on essd-2023-107', Anonymous Referee #2, 09 Aug 2023

This paper presents a sea surface current product at a depth of 15 meters called GEST (Geostrophic-Ekman-Stokes-Tides) and compares it with other surface current products. This work shows some meaningful and interesting results, but there are still critical flaws present. Therefore, I believe that this paper is not suitable for publication in the journal Earth System Science Data, which aims to present original and high-quality datasets.

1) As pointed out by the authors, there are presently similar data products available, such as OSCAR, GEKCO, and the GlobCurrent project. Concerning data precision, GEST does not fundamentally surpass GlobCurrent in terms of enhancement (Figure 14), as the resolution of satellite data remains unaltered. While the inclusion of tidal currents and Stokes drift might enhance accuracy in specific regions (Figure 8), this, however, results in a time span limited to only 2013-2019, which is significantly shorter than the extensive coverage of the traditional dataset (from 1993). Given comparable data accuracy, the study has not presented us with well-founded reasons to exclusively use this product. Personally, I might still favor the use of GlobCurrent (http://globcurrent.ifremer.fr/) which spans over 20 years.

2) The comparison of different velocity combinations in Section 3.5 yields insightful outcomes, clarifying the roles (positive or negative) played by Stokes drift and tidal currents. So, I recommend considering the submission of this paper to an alternative journal, rather than ESSD. In terms of the dataset's intrinsic merit, this study does not yield a novel and compelling product. Additionally, I propose visualizing the results in Table 1 using a bar chart, as it would provide a more intuitive depiction.

3) The authors compare products with 1-degree resolution and 0.25-degree resolution and indicate that the 0.25-degree product better approximates the real ocean currents, which is not a surprising result. Undoubtedly, a 1-degree product cannot capture mesoscale eddies, and its accuracy is certainly lower than that of the 0.25-degree product. This fact is widely recognized and should not constitute the primary conclusion of this paper.

4) L68-70. “In the actual ocean … can be broadly divided into large-scale ocean circulations, micro scale internal waves and storm surges.” This comment appears to lack thorough consideration, as it does not encompass mesoscale and sub-mesoscale processes. While only few observations can directly reflect sub-mesoscale processes, the authors should not dismiss their significant roles in the upper ocean, especially considering the increasing awareness of sub-mesoscale processes in recent years (e.g., JC McWilliams 2016). Relevant discussions are indispensable in this paper. In my view, incorporating sub-mesoscale processes could potentially significantly enhance the data accuracy.

5) The inclusion of explanatory files and variable descriptions is crucial for a well-rounded and usable dataset. I downloaded the data provided by the authors (https://doi.org/10.5281/zenodo.7767202) and performed a preliminary processing. The current state of the dataset, containing only a data matrix in the NC file, is clearly inadequate for effective utilization. I strongly recommend that the authors take the necessary steps to rectify this issue and provide the essential context and information that will significantly enhance the dataset's quality and utility. If the authors truly intends to create a valuable dataset, they should invest more time in the dataset itself. It is evident that they has not drawn upon established exemplary datasets as references, such as (https://data.marine.copernicus.eu/product/MULTIOBS_GLO_PHY_REP_015_004/description).

Citation: https://doi.org/10.5194/essd-2023-107-RC2
- AC2: 'Reply on RC2', Guiyu Wang, 30 Aug 2023
  
  Thanks for your valuable comment. Please find our replies in the attachment.
  
  Citation: https://doi.org/10.5194/essd-2023-107-AC2
EC1:
'Comment on essd-2023-107', Salvatore Marullo, 01 Sep 2023

In addition to what has already been written by the two referees (with whom I fully agree), I would like to point out that the power spectrums shown by the authors leave me very perplexed. One can clearly see that very few points were used for their calculation (a spatial resolution of 0.25 deg means only 40 points over a distance of 10 degrees) and that the interpretation of the resulting effective resolution is wrong for the following reason:
The effective resolution of a spatial or temporal series is not the last point plotted in the PSD figures (the Nyquist frequency I suppose i.e., two times the grid resolution of about 50 km), but the frequency at which the spectrum slope drops down. In this case this is not clear given the few points used to calculate the psd. Perhaps a vague indication of a change of slope could be at wavelengths of about 100 km, but certainly the spectrum shown does not allow this to be stated with certainty. My suggestion is to compute the power spectrum in an area of the ocean where the longest series can be produced, compute a spectrum for each single date and finally average all the spectra. As an example, see figure 2 of Yang et al. “Sea Surface Temperature Intercomparison in the Framework of the Copernicus Climate Change Service (C3S)” available at https://journals.ametsoc.org/view/journals/clim/34/13/JCLI-D-20-0793.1.xml
In addition, the authors should better explain the concept of “training” mentioned in the response to referee 2 not described in the paper. In this regard, I also suggest publishing the entire time series mentioning the period used for the least-squares linear regression.
Considering that, in its current form, this article is between 'major revision' and 'rejected', I suggest that the authors, if they still intend to resubmit a revised version of the article, consider all referee comments very carefully in order to produce a new paper that fully satisfies them.

Citation: https://doi.org/10.5194/essd-2023-107-EC1
- AC3: 'Reply on EC1', Guiyu Wang, 09 Sep 2023
  
  Thanks for your valuable comments and suggestions. Please find our replies in the attachment.
  
  Citation: https://doi.org/10.5194/essd-2023-107-AC3

Status: closed

RC1:
'Comment on essd-2023-107', Anonymous Referee #1, 25 May 2023
Review of the paper
GEST: A multi-scale dynamics-based reconstruction of global ocean surface current
By Guiyu Wang, Ge Chen, Chuanchuan Cao, Xiaoyan Chen , and Baoxiang Huang

General Comments
This paper presents a methodology to reconstruct ocean surface currents optimally combining different components of the ocean surface circulation : geostrophic, Ekman, tidal and wave-induced currents. Scientifically this work is sound, as it aims at providing a global surface currents product which can account locally for significant processes which could be missed relying only on a single/few of the aforementioned surface circulation components. I therefore recommend this paper for publication after considering the following major and minor issues:

Firstly, the metrics for evaluating the goodness of the data are mostly based on direct comparison with in-situ measured currents (drifting buoys), while the authors, already at the abstract level, mention the importance of both “high precision” and “fine resolution”. I think inserting additional analyses (e.g. spectral analyses based on Fast-Fourier-Transform) to evaluate the effective resolution of the GEST dataset could strengthen the manuscript (at least for the analyses presented in section 4.2);

While reading the results, I was concerned by the statistical significance of some of them. As an example, I may provide the specific case reported in figure 14 a. The RMSEs of the different datasets under evaluation are often few tenths of cm/s apart from each other. I was wondering if it is possible to add an information on the confidence level of the different RMSE computation (e.g. via bootstrap analysis). I think it could help readers understand when the GEST RMSE value is confirming the higher accuracy compared to other available surface currents datasets:

I struggled a bit to understand why the Authors wish to provide a dataset with 1°X1° degrees spatial resolution. It was not that clear to me for which purposes/applications it was meant for. Could the Authors please explain?

Specific Comments
I would recommend to further clarify section 3. I honestly struggled a bit to understand that section 3 presents the building blocks of the GEST product. Inserting few lines explaining this concept would be beneficial for the paper;

I think the introduction is lacking part of the effort that has been done to reconstruct surface currents from tracers observations. I thus encourage the authors to consider few additional literature items (e.g. Bowen et al. 2002, Gonzalez-Haro et al. 2014, Liu et al. 2017, Rio and Santoleri 2018 and references therein) and insert few lines in the introduction;

In the manuscript, there are some images (see e.g. figs. 1,3,5) where you claim you are presenting information on 1°x1° boxes. It seems to me the information has somehow been further smoothed spatially. Could the Authors please clarify the reasons behind this choice or, at least, clarify that directly in the text?

A doubt is still related to figure 14 a/c/d: on average, it seems that the overall RMSE of GEST and Globcurrent datasets are equivalent in the latitudinal bands 30-50N and 40-60S, In particular, it seems that GEST and Globcurrent products show alternating better performances in the 30-50N band and equivalent performances in 40-60S band. Such areas are dominated by major current systems, thus relevant for assessing the quality of a surface current product. Could the authors please try to explain further such behaviour? I think it would be useful for users, in order to understand which dataset should be used for a specific study area/application;

Line 152-153: this sentence is unclear to me. Which dataset does not constitute a full independent validation for your reference field? Which reference field are the Authors referring to?

Line 159: What do you mean exactly with “ Ekman layer reaches the position of the drogued drifters position of the drogue drifters”? Are you referring to the vertical position of the drogue? If so, please specify;

Line 186: although one might guess what the Authors mean by “ocean components” I don’t think it is appropriate to mention that one can compare “ocean components and drifter observations. I’d ask the Authors to rephrase the sentence;

Figure 6: The legend should clearly mention what the Authors mean by the blue and red curves. Also, it seems the “Attenuation of experience” and theoretical formula are not precisely mentioned in the manuscript. This makes It hard to intercompare the figure with the findings reported in the text. Could the Authors please further clarify?

Line 203: reading the text it is not simple to understand what the Authors mean by “theoretical formula”. Is this equation 4? Please specify and, in addition, I would provide more details for the “empirical percentage method”, in order to help readers not familiar with that;

Line 224: “Geostrophic currents act as the primary mechanism that form the ocean surface current field”. I do not think it is appropriate to mention that the Geostrophic Currents are a mechanism that generate the ocean current field. I would rather say that they are a component of the total marine currents field;

Line 254: recalling what I mentioned in the “major comments” section. I would ask if the Authors could check whether this 0.3 cm/s RMS difference is significant or not;

Table 1: I would ask the Authors to apply a minor change to the Table: please add the name of each sub-region, in order to help the readers locating the different sub-regions in a global map;

Lines 266-271: would it make sense/be possible for the Authors to add a global map that emphasizes the choice of the different sub-models combinations used for the global reconstruction?

Figure 11/Line 290: I sincerely struggled a bit in understanding the meaning of synthetic vector/optimal vector. Could the Authors please further explain or harmonize the nomenclature of the variables?

Technical Comments
Line 78: Maybe I would say “ and the Globcurrent project products”;

Line 108-110 (and elsewhere if necessary): Please remove the acronym CMEMS , keep Copernicus Marine Service instead;

Line 201: “wavenumber k and wavelength ?” It seems this sentence is unfinished. Could the Authors please double check?

Figure 9: I would add x and y axes labels as Longitude and Latitude while It is redundant to repeat RMSE (cm/s) for each of the four subfigures;

“The OSCAR near-surface current with a grid size of 1°on a 5 days basis use the quasilinear, quasi-steady sea surface momentum equations and improve the equatorial algorithm by fitting…” should be modified as follows: “The OSCAR near-surface currents product, with a grid size of 1°on a 5 days basis, uses the quasilinear, quasi-steady sea surface momentum equations and improves the equatorial algorithm by fitting…”

References
Bowen, M. M., Emery, W. J., Wilkin, J. L., Tildesley, P. C., Barton, I. J., & Knewtson, R. (2002). Extracting multiyear surface currents from sequential thermal imagery using the maximum cross-correlation technique.
Journal of Atmospheric and Oceanic Technology, 19(10), 1665-1676.

González‐Haro, C., & Isern‐Fontanet, J. (2014). Global ocean current reconstruction from altimetric and microwave SST measurements. Journal of Geophysical Research: Oceans, 119(6), 3378-3391.

Liu, J., Emery, W. J., Wu, X., Li, M., Li, C., & Zhang, L. (2017). Computing ocean surface currents from GOCI ocean color satellite imagery. IEEE Transactions on Geoscience and Remote Sensing, 55(12), 7113-7125.

Rio, M. H., & Santoleri, R. (2018). Improved global surface currents from the merging of altimetry and sea surface temperature data. Remote sensing of Environment, 216, 770-785
Citation: https://doi.org/10.5194/essd-2023-107-RC1
- AC1: 'Reply on RC1', Guiyu Wang, 19 Jun 2023
  
  Thank you for your favourable recommendation. Please find our replies in the attachment.
  
  Citation: https://doi.org/10.5194/essd-2023-107-AC1
RC2:
'Comment on essd-2023-107', Anonymous Referee #2, 09 Aug 2023

This paper presents a sea surface current product at a depth of 15 meters called GEST (Geostrophic-Ekman-Stokes-Tides) and compares it with other surface current products. This work shows some meaningful and interesting results, but there are still critical flaws present. Therefore, I believe that this paper is not suitable for publication in the journal Earth System Science Data, which aims to present original and high-quality datasets.

1) As pointed out by the authors, there are presently similar data products available, such as OSCAR, GEKCO, and the GlobCurrent project. Concerning data precision, GEST does not fundamentally surpass GlobCurrent in terms of enhancement (Figure 14), as the resolution of satellite data remains unaltered. While the inclusion of tidal currents and Stokes drift might enhance accuracy in specific regions (Figure 8), this, however, results in a time span limited to only 2013-2019, which is significantly shorter than the extensive coverage of the traditional dataset (from 1993). Given comparable data accuracy, the study has not presented us with well-founded reasons to exclusively use this product. Personally, I might still favor the use of GlobCurrent (http://globcurrent.ifremer.fr/) which spans over 20 years.

2) The comparison of different velocity combinations in Section 3.5 yields insightful outcomes, clarifying the roles (positive or negative) played by Stokes drift and tidal currents. So, I recommend considering the submission of this paper to an alternative journal, rather than ESSD. In terms of the dataset's intrinsic merit, this study does not yield a novel and compelling product. Additionally, I propose visualizing the results in Table 1 using a bar chart, as it would provide a more intuitive depiction.

3) The authors compare products with 1-degree resolution and 0.25-degree resolution and indicate that the 0.25-degree product better approximates the real ocean currents, which is not a surprising result. Undoubtedly, a 1-degree product cannot capture mesoscale eddies, and its accuracy is certainly lower than that of the 0.25-degree product. This fact is widely recognized and should not constitute the primary conclusion of this paper.

4) L68-70. “In the actual ocean … can be broadly divided into large-scale ocean circulations, micro scale internal waves and storm surges.” This comment appears to lack thorough consideration, as it does not encompass mesoscale and sub-mesoscale processes. While only few observations can directly reflect sub-mesoscale processes, the authors should not dismiss their significant roles in the upper ocean, especially considering the increasing awareness of sub-mesoscale processes in recent years (e.g., JC McWilliams 2016). Relevant discussions are indispensable in this paper. In my view, incorporating sub-mesoscale processes could potentially significantly enhance the data accuracy.

5) The inclusion of explanatory files and variable descriptions is crucial for a well-rounded and usable dataset. I downloaded the data provided by the authors (https://doi.org/10.5281/zenodo.7767202) and performed a preliminary processing. The current state of the dataset, containing only a data matrix in the NC file, is clearly inadequate for effective utilization. I strongly recommend that the authors take the necessary steps to rectify this issue and provide the essential context and information that will significantly enhance the dataset's quality and utility. If the authors truly intends to create a valuable dataset, they should invest more time in the dataset itself. It is evident that they has not drawn upon established exemplary datasets as references, such as (https://data.marine.copernicus.eu/product/MULTIOBS_GLO_PHY_REP_015_004/description).

Citation: https://doi.org/10.5194/essd-2023-107-RC2
- AC2: 'Reply on RC2', Guiyu Wang, 30 Aug 2023
  
  Thanks for your valuable comment. Please find our replies in the attachment.
  
  Citation: https://doi.org/10.5194/essd-2023-107-AC2
EC1:
'Comment on essd-2023-107', Salvatore Marullo, 01 Sep 2023

In addition to what has already been written by the two referees (with whom I fully agree), I would like to point out that the power spectrums shown by the authors leave me very perplexed. One can clearly see that very few points were used for their calculation (a spatial resolution of 0.25 deg means only 40 points over a distance of 10 degrees) and that the interpretation of the resulting effective resolution is wrong for the following reason:
The effective resolution of a spatial or temporal series is not the last point plotted in the PSD figures (the Nyquist frequency I suppose i.e., two times the grid resolution of about 50 km), but the frequency at which the spectrum slope drops down. In this case this is not clear given the few points used to calculate the psd. Perhaps a vague indication of a change of slope could be at wavelengths of about 100 km, but certainly the spectrum shown does not allow this to be stated with certainty. My suggestion is to compute the power spectrum in an area of the ocean where the longest series can be produced, compute a spectrum for each single date and finally average all the spectra. As an example, see figure 2 of Yang et al. “Sea Surface Temperature Intercomparison in the Framework of the Copernicus Climate Change Service (C3S)” available at https://journals.ametsoc.org/view/journals/clim/34/13/JCLI-D-20-0793.1.xml
In addition, the authors should better explain the concept of “training” mentioned in the response to referee 2 not described in the paper. In this regard, I also suggest publishing the entire time series mentioning the period used for the least-squares linear regression.
Considering that, in its current form, this article is between 'major revision' and 'rejected', I suggest that the authors, if they still intend to resubmit a revised version of the article, consider all referee comments very carefully in order to produce a new paper that fully satisfies them.

Citation: https://doi.org/10.5194/essd-2023-107-EC1
- AC3: 'Reply on EC1', Guiyu Wang, 09 Sep 2023
  
  Thanks for your valuable comments and suggestions. Please find our replies in the attachment.
  
  Citation: https://doi.org/10.5194/essd-2023-107-AC3

Guiyu Wang, Ge Chen, Chuanchuan Cao, Xiaoyan Chen, and Baoxiang Huang

Data sets

GEST Ocean Surface Current Guiyu Wang https://doi.org/10.5281/zenodo.7767202

Guiyu Wang, Ge Chen, Chuanchuan Cao, Xiaoyan Chen, and Baoxiang Huang

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Short summary

We present an accurate product of ocean surface current at 15 m depth based on multi-scale physical processes. Following a training process using remote sensing observations and in situ data, the derived current field with a 1/4° resolution captures more details neglected in the 1° ones and demonstrates higher accuracy over other global surface current products at low to middle latitudes.


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